We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equ...We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.展开更多
Quantum dynamics of a charged particle in a two-dimensional （2D） lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations （the case of vanishing electric fiel...Quantum dynamics of a charged particle in a two-dimensional （2D） lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations （the case of vanishing electric field） and Bloch oscillations （zero magnetic field）, details of which has not yet been com- pletely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional （1D） model which can be easily realized in labora- tory experiments with quasi-lD optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.展开更多
The optical Bloch oscillation(OBO)is an optical-quantum analogy effect that is significant for light field manipulations,such as light beam localization,oscillation and tunneling.As an intra-band oscillation,OBO was i...The optical Bloch oscillation(OBO)is an optical-quantum analogy effect that is significant for light field manipulations,such as light beam localization,oscillation and tunneling.As an intra-band oscillation,OBO was important for optical investigations in photonic lattices and atomic vapors over an extended period of time.However,OBO in reconfigurable platforms is still an open topic,even though tunability is highly desired in developing modern photonic techniques.Here we theoretically establish and experimentally demonstrate OBO in an electromagnet-ically induced photonic lattice with a ramping refractive index,established in a coherently-prepared three-level 85 Rb atomic vapor under the electromagnetically induced transparency condition.This is achieved by interfering two coupling beams with Gaussian profiles and launching a probe beam that exhibits OBO within the resulting lattice.The induced reconfigurable photonic lattice possesses a transverse gradient,due to the innate edges of Gaussian beams,and sets a new stage for guiding the flow of light in periodic photonic environments.Our results should motivate better understanding of peculiar physical properties of an intriguing quantum-optical analogy in an atomic setting.展开更多
We theoretically investigate high-order harmonic generation(HHG)in crystals induced by linearly polarized laser fields.We obtain the HHG spectra by solving the semiconductor Bloch equations and analyze the radiation p...We theoretically investigate high-order harmonic generation(HHG)in crystals induced by linearly polarized laser fields.We obtain the HHG spectra by solving the semiconductor Bloch equations and analyze the radiation process by different models.Here we propose a multiple collision model,in which the electrons and holes are produced at different times and places.It is found that the multiple collision trajectories can help us comprehensively and better explain the results of the quantum calculation.Moreover,we find that the harmonic suppression occurs due to the overlap of multiple collision trajectories.展开更多
The conduction of a single-wall carbon nanotube depends on the pitch. If there are an integral number of carbon hexagons per pitch, then the system is periodic along the tube axis and allows “holes” (not “electrons...The conduction of a single-wall carbon nanotube depends on the pitch. If there are an integral number of carbon hexagons per pitch, then the system is periodic along the tube axis and allows “holes” (not “electrons”) to move inside the tube. This case accounts for a semiconducting behavior with the activation energy of the order of around 3 meV. There is a distribution of the activation energy since the pitch and the circumference can vary. Otherwise nanotubes show metallic behaviors (significantly higher conductivity). “Electrons” and “holes” can move in the graphene wall (two dimensions). The conduction in the wall is the same as in graphene if the finiteness of the circumference is disregarded. Cooper pairs formed by the phonon exchange attraction moving in the wall is shown to generate a temperature-independent conduction at low temperature (3 - 20 K).展开更多
Individual metallic single-wall carbon nanotubes show unusual non-Ohmic transport behaviors at low and high bias fields. For low-resistance contact samples, the differential conductance increases with increasing bias,...Individual metallic single-wall carbon nanotubes show unusual non-Ohmic transport behaviors at low and high bias fields. For low-resistance contact samples, the differential conductance increases with increasing bias, reaching a maximum at ~100 mV. As the bias increases further, drops dramatically [1]. The higher the bias, the system behaves in a more normal (Ohmic) manner. This low-bias anomaly is temperature-dependent (50 - 150 K). We propose a new interpretation. Supercurrents run in the graphene wall below ~150 K. The normal hole currents run on the outer surface of the wall, which are subject to the scattering by phonons and impurities. The currents along the tube length generate circulating magnetic fields and eventually destroy the supercurrent in the wall at high enough bias, and restore the Ohmic behavior. If the prevalent ballistic electron model is adopted, then the temperature-dependent scattering effects cannot be discussed. For the high bias (0.3 - 5 V), (a) the I-V curves are temperature-independent (4 - 150 K), and (b) the currents (magnitudes) saturate. The behavior (a) arises from the fact that the neutral supercurrent below the critical temperature is not accelerated by the electric field. The behavior (b) is caused by the limitation of the number of quantum-states for the “holes” running outside of the tube.展开更多
Magnetic resonance imaging(MRI), magnetic resonance angiography(MRA) and magnetic resonance spectroscopy(MRS) are fundamental concepts used in modern medicine to improve health care. These concepts are based on the pr...Magnetic resonance imaging(MRI), magnetic resonance angiography(MRA) and magnetic resonance spectroscopy(MRS) are fundamental concepts used in modern medicine to improve health care. These concepts are based on the principle of nuclear magnetic resonance(NMR). Over the years, various laboratories around the world have applied different numerical techniques based on the Bloch NMR equations to solve specific problems in physics, biology, chemistry, engineering and medicine. The ultimate goal of any physician is to obtain maximum physical, biophysical, chemical and biological information on any tissue or cell under examination. This goal can be achieved by solving the Bloch NMR flow equations analytically. In this review, we present the basic principle of NMR/MRI in a way that can be easily understood by any researcher who needs an NMR concept to solve a specific medical problems. After a very brief history of the subject, a second order, non homogeneous, time-dependent differential equation derived from the Bloch NMR equation is presented. This equation has the basic intrinsic properties of MRI, MRA and MRS that can be extracted by means of classical and quantum mechanics for possible application in nanomedicine.展开更多
The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordi...The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.展开更多
基金supported in part by Department of Energy under Contract No.DE-FG02-03ER25587by Office of Naval Research under Contract No.N00014-01-1-0674by National Science Foundation grant DMS-0708026
文摘We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.
文摘Quantum dynamics of a charged particle in a two-dimensional （2D） lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations （the case of vanishing electric field） and Bloch oscillations （zero magnetic field）, details of which has not yet been com- pletely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional （1D） model which can be easily realized in labora- tory experiments with quasi-lD optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.
基金This work was supported by National Key R&D Program of China(Grants No.2018YFA0307500,2017YFA0303703)National Natural Science Foundation of China(Grants No.62022066,12074306,61975159,and 12074308)Work in Qatar is supported by the NPRP 11S-1126-170033 project from the Qatar National Research Fund.
文摘The optical Bloch oscillation(OBO)is an optical-quantum analogy effect that is significant for light field manipulations,such as light beam localization,oscillation and tunneling.As an intra-band oscillation,OBO was important for optical investigations in photonic lattices and atomic vapors over an extended period of time.However,OBO in reconfigurable platforms is still an open topic,even though tunability is highly desired in developing modern photonic techniques.Here we theoretically establish and experimentally demonstrate OBO in an electromagnet-ically induced photonic lattice with a ramping refractive index,established in a coherently-prepared three-level 85 Rb atomic vapor under the electromagnetically induced transparency condition.This is achieved by interfering two coupling beams with Gaussian profiles and launching a probe beam that exhibits OBO within the resulting lattice.The induced reconfigurable photonic lattice possesses a transverse gradient,due to the innate edges of Gaussian beams,and sets a new stage for guiding the flow of light in periodic photonic environments.Our results should motivate better understanding of peculiar physical properties of an intriguing quantum-optical analogy in an atomic setting.
基金Project supported by the National Natural Science Foundation of China(Grant No.91850121)the K.C.Wong Education Foundation(Grant No.GJTD-2019-15)
文摘We theoretically investigate high-order harmonic generation(HHG)in crystals induced by linearly polarized laser fields.We obtain the HHG spectra by solving the semiconductor Bloch equations and analyze the radiation process by different models.Here we propose a multiple collision model,in which the electrons and holes are produced at different times and places.It is found that the multiple collision trajectories can help us comprehensively and better explain the results of the quantum calculation.Moreover,we find that the harmonic suppression occurs due to the overlap of multiple collision trajectories.
文摘The conduction of a single-wall carbon nanotube depends on the pitch. If there are an integral number of carbon hexagons per pitch, then the system is periodic along the tube axis and allows “holes” (not “electrons”) to move inside the tube. This case accounts for a semiconducting behavior with the activation energy of the order of around 3 meV. There is a distribution of the activation energy since the pitch and the circumference can vary. Otherwise nanotubes show metallic behaviors (significantly higher conductivity). “Electrons” and “holes” can move in the graphene wall (two dimensions). The conduction in the wall is the same as in graphene if the finiteness of the circumference is disregarded. Cooper pairs formed by the phonon exchange attraction moving in the wall is shown to generate a temperature-independent conduction at low temperature (3 - 20 K).
文摘Individual metallic single-wall carbon nanotubes show unusual non-Ohmic transport behaviors at low and high bias fields. For low-resistance contact samples, the differential conductance increases with increasing bias, reaching a maximum at ~100 mV. As the bias increases further, drops dramatically [1]. The higher the bias, the system behaves in a more normal (Ohmic) manner. This low-bias anomaly is temperature-dependent (50 - 150 K). We propose a new interpretation. Supercurrents run in the graphene wall below ~150 K. The normal hole currents run on the outer surface of the wall, which are subject to the scattering by phonons and impurities. The currents along the tube length generate circulating magnetic fields and eventually destroy the supercurrent in the wall at high enough bias, and restore the Ohmic behavior. If the prevalent ballistic electron model is adopted, then the temperature-dependent scattering effects cannot be discussed. For the high bias (0.3 - 5 V), (a) the I-V curves are temperature-independent (4 - 150 K), and (b) the currents (magnitudes) saturate. The behavior (a) arises from the fact that the neutral supercurrent below the critical temperature is not accelerated by the electric field. The behavior (b) is caused by the limitation of the number of quantum-states for the “holes” running outside of the tube.
文摘Magnetic resonance imaging(MRI), magnetic resonance angiography(MRA) and magnetic resonance spectroscopy(MRS) are fundamental concepts used in modern medicine to improve health care. These concepts are based on the principle of nuclear magnetic resonance(NMR). Over the years, various laboratories around the world have applied different numerical techniques based on the Bloch NMR equations to solve specific problems in physics, biology, chemistry, engineering and medicine. The ultimate goal of any physician is to obtain maximum physical, biophysical, chemical and biological information on any tissue or cell under examination. This goal can be achieved by solving the Bloch NMR flow equations analytically. In this review, we present the basic principle of NMR/MRI in a way that can be easily understood by any researcher who needs an NMR concept to solve a specific medical problems. After a very brief history of the subject, a second order, non homogeneous, time-dependent differential equation derived from the Bloch NMR equation is presented. This equation has the basic intrinsic properties of MRI, MRA and MRS that can be extracted by means of classical and quantum mechanics for possible application in nanomedicine.
文摘The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.
